Re: Proving Linear Algebra

The key is to prove the two definations of dot product are equivalent.Def1: dot product is the sum of corresponding cartesian co-ordinates.Def2: dot product is the product of two vector lenths, and the cosine of their angle.

Usually this is proved within a triangle consisting of vector OA, OB, and AB=OB-OA

In a catesian system, distance formula is true based on Pythagoras' Theorem.

So if you define A(x[sub]1[/sub],y[sub]1[/sub],z[sub]1[/sub]) B(x[sub]2[/sub] ,y[sub]2[/sub],z[sub]2[/sub]), you get